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Mathematical Constants
Intriguing, ubiquitous, and at times mysterious, numerical constants set the allowable limits for all universal phenomena. Whether your questions involves π, Avogadro's number, Planck's constant, the atomic mass unit, or any of the other multitudes of immutable numbers used in science, this is the category where they should be asked.
2,332 Questions
Why you restrict the argument of a complex number between -pi and pi?
Restricting the argument of a complex number between -π and π is a common practice because it allows for a unique representation of the number in polar form. This range ensures that the principal argument lies within one full rotation in the complex plane, simplifying calculations involving angles and trigonometric functions. Additionally, it helps avoid ambiguity and ensures consistency in mathematical operations involving complex numbers.
What is anacrusis triplet and quartet?
An anacrusis, also known as a pickup or upbeat, is a note or series of notes that precede the first downbeat of a piece of music. It helps establish the meter and prepare the listener for the beginning of the music. A triplet is a rhythmic grouping of three notes played in the time of two, while a quartet is a group of four musicians playing together. Triplets and quartets are common rhythmic and ensemble configurations in music performance.
What is between the Roman numerals XL and LX?
Roman numerals XL is 40, and LX is 60. Numbers in-between are XLI, XLII, XLIII, XLIV. XLV, XLVI, XLVII, XLVIII, XLVIX, L, LI, LII, LIII, LIV. LV. LVI, LVII, ;LVIII, and LVIX.
Is pi the biggest number in the world?
Pi is not the biggest number in the world, just one of the longest.
It shares that honor with all the other 'repeating' or 'recurring' decimals. These are decimals that go on into infinity and never stop.
How many zeros does 150 million have?
150 million has six zeros. This is because a million is equal to 1,000,000, which has six zeros. Therefore, when we have 150 million, we have 150 multiplied by 1 million, which gives us 150,000,000, with six zeros.
What is the number of moles of 200g of Fe?
For this you need the atomic (molecular) mass of FeCl3. Take the number of moles and multiply it by the atomic mass. Divide by one mole for units to cancel. FeCl3=162.4 grams
.200 moles FeCl3
Often, in mathematical problems, you are asked to find out an unknown value. Towards that end, you are "given" some numbers to assist in that process.
What are the cube roots of an imaginary number in trigonometric form?
z = y i where y is a real number
1: z^(1/3) = y^(1/3) (cos(30 deg) + i sin(30 deg))
2: z^(1/3) = y^(1/3) (-sin(60 deg) + i cos(60 deg))
3: z^(1/3) = y^(1/3) (- i)
What is the twenty seventh power of an imaginary number?
See the Wikipedia article on Imaginary Numbers. i^n = i^(n mod 4). With n = 27, 27 mod 4 = 3, and i^3 = -i. This is easier to visualize when you consider the graphical representation of complex numbers, and use polar coordinates. Writing i as exp(i*pi/2), (from Euler's formula), then i^27 = {using exp() to mean the natural base e, raised to a power} exp(i*pi/2)^27 = exp(27*i*pi/2) = exp(13.5*i*pi) = exp((12 + 1.5)*(i*pi)) = exp(12*i*pi)*exp(3*i*pi/2).
Since the coefficient of i in the exponent is an angle (in radians), then even multiples of pi are the same angle as 0 {exp(0) = 1} so we are back to the same as exp(3*i*pi/2), which is pointing straight down [-i]. Note that 3*pi/2 radians is the same as 270°.
Since the question asked about 27th power of an imaginary number, that could mean a multiple of i, such as bi, where b is any real number. In this case, you would have (bi)^27 = (b^27)(i^27) = (b^27)(-i). So if b = 1.5 for example, then you would have (-i)(1.5^27) ≅ -56815i.
Is graham number beyond all finite transfinite and transinfinite numbers?
Graham's number is a large but finite number. Therefore it is less than every transfinite cardinal number. "Transinfinite" doesn't make sense.
What numbers are in pi and how many are there?
Pi is the ratio of the circumference of a circle to its diameter. Pi is 3.1415926535897932384626433832795 but some just use 3.14
The canonical example is the square root of -1.
Mathematicians use the symbol i to represent it, electrical engineers use j because i is already busy.
Can Planck's constant is zero?
No. It is a very small number (approximately 6.626 × 10-34 joule-second) but that is NOT zero
Do ANY number series in pi repeat themselves?
There are short strings of digits which will repeat, but there is no sequence which will repeat forever.
Why you call zero by the name zero?
The derivation is from the early 17th cent.: from French zéro or Italian zero, via Old Spanish from Arabic ṣifr 'cipher.'
What is the solution to 30X to 29Y?
"30X to 29Y" is not an equation nor an inequality. There is, therefore, not a mathematical solution to the question.
